The labels in medical diagnosis task are usually discrete and successively distributed. For example, the Diabetic Retinopathy Diagnosis (DR) involves five health risk levels: no DR (0), mild DR (1), moderate DR (2), severe DR (3) and proliferative DR (4). This labeling system is common for medical disease. Previous methods usually construct a multi-binary-classification task or propose some reparameter schemes in the output unit. In this paper, we target on this task from the perspective of loss function. More specifically, the Wasserstein distance is utilized as an alternative, explicitly incorporating the inter-class correlations by pre-defining its ground metric. Then, the ground metric which serves as a linear, convex or concave increasing function w.r.t. the Euclidean distance in a line is explored from an optimization perspective.Meanwhile, this paper also proposes of constructing the smoothed target labels that model the inlier and outlier noises by using a unimodal-uniform mixture distribution. Different from the one-hot setting, the smoothed label endues the computation of Wasserstein distance with more challenging features. With either one-hot or smoothed target label, this paper systematically concludes the practical closed-form solution. We evaluate our method on several medical diagnosis tasks (e.g., Diabetic Retinopathy and Ultrasound Breast dataset) and achieve state-of-the-art performance.

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Semantic segmentation (SS) is an important perception manner for self-driving cars and robotics, which classifies each pixel into a pre-determined class. The widely-used cross entropy (CE) loss-based deep networks has achieved significant progress w.r.t. the mean Intersection-over Union (mIoU). However, the cross entropy loss can not take the different importance of each class in an self-driving system into account. For example, pedestrians in the image should be much more important than the surrounding buildings when make a decisions in the driving, so their segmentation results are expected to be as accurate as possible. In this paper, we propose to incorporate the importance-aware inter-class correlation in a Wasserstein training framework by configuring its ground distance matrix. The ground distance matrix can be pre-defined following a priori in a specific task, and the previous importance-ignored methods can be the particular cases. From an optimization perspective, we also extend our ground metric to a linear, convex or concave increasing function w.r.t. pre-defined ground distance. We evaluate our method on CamVid and Cityscapes datasets with different backbones (SegNet, ENet, FCN and Deeplab) in a plug and play fashion. In our extenssive experiments, Wasserstein loss demonstrates superior segmentation performance on the predefined critical classes for safe-driving.

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